F-stops, T-stops, focal length and lens aperture

The focal length of a lens is the distance between the optical center of the lens and the film plane (for film cameras) or CCD (for camcorders). The longer the focal length, the more it “magnifies” the subject.

f-stops are a measure of the aperture of a lens. In other words, f-stops tell us how wide open the iris of a lens is. Specifically, they express the ratio of focal length to apparent lens aperture, so they have no units. The smaller the number, the wider the effective aperture, and the more light will go through the lens. Hence f2.0 is a wide aperture, whereas f11.0 is a narrow aperture.

The relationship between f-stop, focal length and the diameter of the lens opening is as follows:

f-stop = focal length / diameter of lens opening

Thus a 50mm lens with an iris diameter of 25mm has an aperture of 50 / 25 = f2.0

In practice f-stops have discrete values; in other words, lenses have a finite number of f-stops available, with no intermediate options. The standard f-stops are as follows:

1.0 | 1.4 | 2.0| 2.8 | 4 | 5.6 | 8 | 11 | 16 | 22

Reducing the f-stop of a lens (increasing its aperture) has three effects:

* more light goes through the lens, increasing the exposure;

* the depth of field decreases, making the background more blurred;

* the overall sharpness of the image decreases, and chromatic aberration is enhanced. This is an inevitable consequence of having a wider aperture. However, if you are shooting on video, especially when using a 1/3” CCD camera, you should consistently use a wide aperture if you want a shallow depth of field, resorting to the use of neutral density filters when necessary.

The relationship between f-stop and exposure is not linear. If you open the iris of the lens by one stop, you are doubling the amount of light that goes through. Conversely, reducing the aperture by one stop halves the exposure (other things being equal). Opening the iris by two stops increases the exposure by a factor of four, opening it by three stops brightens the image by a factor of eight, and so on.

This explains the standard sequence of f-stops shown above, which may seem arbitrary, but in fact makes perfect mathematical sense: since it is the area of the lens opening that determines how much light goes through, to double the area we must divide the f-number by the square root of 2, which is approximately 1.414 – hence the weird numbers. (This is because area is proportional to the square of linear dimensions.)

You can check this yourself by verifying that to go from an f-stop to one of its neighbors you multiply or divide by approximately 1.414.

Mathematical considerations aside, the thing to remember about f-stops is that they refer to lens aperture relative to focal length, and that they are also used to refer to the illumination of a subject: if we say an actor’s face is one stop underexposed, it typically means that we should double the illumination of the actor’s face – we should add one stop’s worth of lighting to it.

Constant f-stop while zooming

As noted above, the vale of the f-stop depends on the apparent diameter of the lens. The apparent aperture diameter depends on the magnification of the lens. For example, an aperture that is 50mm wide might look 100mm wide as a result of the lens elements in front of it; the apparent diameter of the iris diaphragm is what matters when calculating F-stops.

This means of course that when you zoom in (increase the focal length of the lens), the apparent aperture increases, since it is being magnified. However, since the value of the f-stop is the ratio between focal length and apparent aperture, the f-stop also stays approximately constant.

Zoom lenses are designed in such a way that when you zoom in or out, the change in focal length exactly compensates the change in the apparent aperture. Hence there is no difference in exposure when you zoom in or out.

T-stops

In practice, even the best lenses exhibit light absorbance, effectively “stealing” some of the light going through them. This means that if you calculate the exposure based on the f-stop of the lens, you will end up underexposing the image, because less light is reaching the film plane than is expected in theory. T-stops are the f-stop of the lens corrected for its absorbance and reflectance. The T-stop is the true speed of the lens, calculated by compensating for its light absorbance and reflectance, and will result in accurate exposure.

Lens speed

The speed rating of a lens, expressed as an f-top or T-stop, is its maximum aperture. It is known as “speed” because it affects how long it would take to achieve correct exposure on a film of a given ISO rating. Fast lenses have a large maximum aperture (e.g. f2.0) and allow a faster exposure time for a given film sensitivity (ISO rating).

Zoom lenses tend to be slower than prime lenses, since they tend to be quite long and it would require an impractical lens diameter to maintain a low f-stop. For example, a 50mm lens with a speed of f1.0 would need to have an iris diaphragm that is 50mm wide. That’s perfectly attainable.

On the other hand, if you want a 250mm lens with a speed of f1.0, its apparent iris diameter would have to be 250mm, which is impractical and expensive.

In response to Martin and Anirudh, it is better to understand that the arithmetical f stop is a constant and so in any depth of field calculations the correct result will be obtained.

The T stop is a measure of the ACTUAL light transmittance of a lens as explained by LAvideoFilmmaker. Because of light losses as photons get absorbed by lens elements and reflected by each glass to air surface, the actual “speed” of the lens will always be slower. This is vitally important to know when calculating exposure, but is inaccurate for depth of field calculations.

It is important in exposure applications where metering is not TTL by the camera, but metering is made externally by, say, a highly accurate hand-held spot meter. Using such a meter you will readily see that if the meter is set to f1.4 but the T value is f1.7, as could happen with older cheaper lenses, then the resultant image will be under-exposed by a full half a stop.

T values don’t add any value when the camera itself carries out the metering via its TTL capability as the meter automatically takes into account the actual light passing through the lens. So you could say, metering is carried out on the actual T value, even though you will never know what the T value of your lens is.

A good reason why all lenses are not calibrated in T values, is because it costs money for each lens to be calibrated and because most stills photographers have TTL metering, it isn’t necessary, as explained in the previous paragraph.

If your work necessitates a T calibrated lens, then you will sure find out, and a purchase becomes mandatory. Except for specific professional applications, where accurate exposure is critical, they aren’t really necessary for the majority of photographers.

I would add that the other time the “T” factor for a lens is important is when buying a new lens for low-light or high-speed applications. Not all f/1.4 lenses have the same ‘T’ factor, so if you have a f/1.8 lens with a good ~95% ‘T’ factor, getting a new cheap f/1.4 might increase the depth-isolation (which may be better or worse for your photos) but actually *decrease* the light reaching your camera (requiring a slower-speed shutter or higher ISO to compensate).

Also, it is a key factor in understanding why you don’t get the “great” pictures in a zoom lens that you can in a prime lens (95% t factor versus a 65-70% t factor makes a LOT of difference), and can help guide in the field as to when you should switch to a prime lens (and do minor reframing in post) instead of sticking with a zoom (ad getting a tight framing in camera).

Generally, I’d look for the t-factor (the minimum t-stop relative to the minimum f-stop) given at a site like dxomark.

I would add a side note for the statement in the original article that: “Zoom lenses are designed in such a way that when you zoom in or out, the change in focal length exactly compensates the change in the apparent aperture. Hence there is no difference in exposure when you zoom in or out.” I would say this is a design goal which some lenses achieve in full, and others achieve partially, with a longer zoom typically yielding a smaller aperture and thus a larger f-stop number. In the marketplace there are variable zoom lenses that maintain constant f-stop (aperture) and ones that don’t. The first category is usually quite a LOT more expensive to buy. For example, the Canon 70-300 4-5.6 EF IS USM is in the $400 range while the constant-2.8 F-stop 80-200 f2.8L is in the $2000 range. There are also $1000-plus L-series lenses that don’t have constant f-stop, but there are no Canon lenses under $1000 that DO have constant f-stop. Sounds like you have expensive tastes, sir! Great article all around though. Thanks!